How do I rotate and scale edges in Edit Mode?
The Transform panel in the Properties tab is only for moving mesh elements.
In Edit mode, you can transform the mesh using the Properties tab. In the top right of the Properties tab, you can see a Transform panel.



With mesh elements selected you can move them by Transform tab. Like you said, they only allow you to move them.



If you want to scale and rotate you use transform menu in the tool tab. Press T to open the tool tab. On the top left you will see the Transform panel.



You can click on this to interactively move mesh elements. After that, you can revise it in the Operator tab at the bottom of the tool tab.

     



The most popular method of doing these transforms is with the keyboard shortcuts. Using the keyboard shortcuts instead of the GUI is a lot faster and will speed up your workflow. With your cursor in the 3d view you can do:

G: grab, aka. move or translate

R: rotate

S: scale

You can also specify an axis for the transform by pressing X or Y or Z once you are in one of the transform modes. You can exclude an axis from the transform by pressing Shift+axis.
You can specify the exact amount of transform by pressing the numbers once in transform mode.

Some examples:

G, X, 2 move 2 units along x axis

R,Shift+Z,90 rotate 90 degrees along the x and y axis

S, 2 scale by a factor of 2